Abstract
Multi-compartment models in diffusion MRI (dMRI) are used to describe complex white matter fiber architecture of the brain. In this paper, we propose a novel multi-compartment estimation method based on the ball-and-stick model, which is composed of an isotropic diffusion compartment (“ball”) as well as one or more perfectly linear diffusion compartments (“sticks”). To model the noise distribution intrinsic to dMRI measurements, we introduce a Rician likelihood term and estimate the model parameters by means of an Expectation Maximization (EM) algorithm. This paper also addresses the problem of selecting the number of fiber compartments that best fit the data, by introducing a sparsity prior on the volume mixing fractions. This term provides automatic model selection and enables us to discriminate different fiber populations. When applied to simulated data, our method provides accurate estimates of the fiber orientations, diffusivities, and number of compartments, even at low SNR, and outperforms similar methods that rely on a Gaussian noise distribution assumption. We also apply our method to in vivo brain data and show that it can successfully capture complex fiber structures that match the known anatomy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Tournier, Calamante, F., Gadian, D.G., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage 23(3), 1176–1185 (2004)
Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical Q-ball imaging. Magn. Res. Med. 58(3), 497–510 (2007)
Tuch, D.S., Reese, T.G., Wiegell, M.R., Wedeen, V.J.: Diffusion MRI of Complex Neural Architecture. Neuron 40(5), 885–895 (2003)
Behrens, T.E., Berg, H.J., Jbabdi, S., Rushworth, M.F., Woolrich, M.W.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34(1), 144–155 (2007)
Liu, C., Bammer, R., Acar, B., Moseley, M.E.: Characterizing non-gaussian diffusion by using generalized diffusion tensors. Magn. Reson. Med. 51(5), 924–937 (2004)
Weldeselassie, Y.T., Barmpoutis, A., Atkins, M.S.: Symmetric positive-definite cartesian tensor orientation distribution functions (CT-ODF). In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010, Part I. LNCS, vol. 6361, pp. 582–589. Springer, Heidelberg (2010)
Jiao, F., Gur, Y., Johnson, C.R., Joshi, S.: Detection of crossing white matter fibers with high-order tensors and rank-k decompositions. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 538–549. Springer, Heidelberg (2011)
Behrens, T.E.J., Woolrich, M.W., Jenkinson, M., Johansen-Berg, H., Nunes, R.G., Clare, S., Matthews, P.M., Brady, J.M., Smith, S.M.: Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magn. Reson. Med. 50(5), 1077–1088 (2003)
Hosey, T., Williams, G., Ansorge, R.: Inference of multiple fiber orientations in high angular resolution diffusion imaging. Magn. Reson. Med. 54(6), 1480–1489 (2005)
Caan, M., Khedoe, H., Poot, D., den Dekker, A., Olabarriaga, S., Grimbergen, K., van Vliet, L., Vos, F.: Estimation of diffusion properties in crossing fiber bundles. IEEE Transactions on Medical Imaging 29(8), 1504–1515 (2010)
Schultz, T., Westin, C.-F., Kindlmann, G.: Multi-diffusion-tensor fitting via spherical deconvolution: A unifying framework. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010, Part I. LNCS, vol. 6361, pp. 674–681. Springer, Heidelberg (2010)
Marzetta, T.L.: EM algorithm for estimating the parameters of a multivariate complex Rician density for polarimetric SAR. In: 1995 International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 3651–3654. IEEE (1995)
Scherrer, B., Warfield, S.K.: Why multiple b-values are required for multi-tensor models. Evaluation with a constrained log-Euclidean model. In: Proc. of the 7th IEEE International Symposium on Biomedical Imaging (ISBI), pp. 1389–1392 (2010)
Cook, P., Bai, Y., Nedjati-Gilani, S., Seunarine, K., Hall, M., Parker, G., Alexander, D.: Camino: Open-source diffusion-mri reconstruction and processing. In: 14th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, vol. 2759 (2006)
Alexander, D., Barker, G., Arridge, S.: Detection and modeling of non-gaussian apparent diffusion coefficient profiles in human brain data. Magnetic Resonance in Medicine 48(2), 331–340 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhu, X., Gur, Y., Wang, W., Fletcher, P.T. (2013). Model Selection and Estimation of Multi-compartment Models in Diffusion MRI with a Rician Noise Model. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds) Information Processing in Medical Imaging. IPMI 2013. Lecture Notes in Computer Science, vol 7917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38868-2_54
Download citation
DOI: https://doi.org/10.1007/978-3-642-38868-2_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38867-5
Online ISBN: 978-3-642-38868-2
eBook Packages: Computer ScienceComputer Science (R0)